If you were to be homeless, yet stay in your home country, and was limited to bring one backpack worth of stuff what would your bring?

What fits in a backpack? Probably a change of clothes (jeans, shirt, socks, underwear), roll of toilet paper, maybe a pack of baby wipes, computer. It would be pretty heavy with those things.

I went to Alaska this summer and so we had our luggage we checked with the airline and the backpack for carryon, and with the computer, ID, some things to read, a few minor things the backpack was probably 20 lbs.

Laptop
Phone
Charging cables
Toiletries
7 casual, interchangeable outfits
Sneakers
Boots
Gloves & scarf
Coat
Daily meds & pills

I’d move into my car (assuming I can at least afford to run that) and sleep in my office at work (assuming I’m partially employed).

Option 2 is to sleep in my car in the parking lot of a local library that has overnight parking, a really strong, free WiFi signal that extends outside, and large, private bathrooms. I’d hangout in the library mostly during the day.

I might not have a home, but I could still teach online and stay partially employed.

And yes, I’ve put a lot of thought into this over the years.

If it’s a car, I have an SUV so I can load a whole lot in there. I answered as per the OP’s directive, which was backpack.

I think the limiting factor in this is not how much can you cram into a backpack, it’s how much can you carry. I had 2 US Army backpacks, one for me and one for my wife. I packed them up with things I might need to survive and had to stop when mine weighed 80 pounds (36.3 kg for those on the metric). My wife, being much smaller, had to stop at about 30–40 pounds

When we decided to pack, we were picturing having to live outside for an extended period of time. Things we packed were:

Tent with ground cloth (tarp)
sleeping bags
fire starting materials
rope
knives
compass
compressed/dried food
water purification stuff and canteens
books on foraging and plant identification
tools that might help us such as a survival shovel and a Leatherman tool
stuff to cook food – camp cook pot, cutlery, etc
Medicines my wife needed
A well stocked first aid kit
something to repel mosquitos and ticks as well as treating bites.
Something to do for entertainment – pad and paper, books, dice.
Extra socks and underwear
two changes of clothes and some way to wash what we had.
Toilet paper. We have since upgraded this to compressed towels (Discs about the size of 4 quarters stacked that, when you add water, expand to be a towel about the size of a washcloth.)
Primitive fishing equipment
Money (cash, silver and gold)

Some things like a rain jacket or winter wear we would just wrap around our waists so as to not take up space in the pack.

That was a big load. Some things are bulky but not heavy, others are heavy but no bulky, some are both. It wouldn’t be enough to live indefinitely but it would be enough to survive for quite a while.

I first need to know where I will be as my needs will vary depending on location.
That said I will take a bag of money in that currency.